I have tried placing both the server certificate and the intermediate
certificate in the same file. OpenLDAP won't start if I put the
intermediate certificate first, and openssl fails to verify the
certificate chain if I put the server certificate first in the file.
Have I missed something obvious or has OpenLDAP really forced me into
the position of needing to add the intermediate certificate from my SSL
CA Vendor into my trusted store on all my clients?

It's a CA cert; have you tried adding it to the file specified by the
TLSCACertificateFile option?

Well, I never looked at it that way. Yes, adding the intermediate
certificate to the file pointed to by the TLSCACertificateFile option on
the OpenLDAP server appears to have worked.

Amaazing what trouble you could save yourself if you actually read the
documentation.